250 research outputs found
Rich Variety of Bifurcations and Chaos in a Variant of Murali-Lakshmanan-Chua Circuit
A very simple nonlinear parallel nonautonomous LCR circuit with Chua's diode
as its only nonlinear element, exhibiting a rich variety of dynamical features,
is proposed as a variant of the simplest nonlinear nonautonomous circuit
introduced by Murali, Lakshmanan and Chua(MLC). By constructing a two-parameter
phase diagram in the plane, corresponding to the forcing amplitude
(F) and frequency , we identify, besides the familiar period-doubling
scenario to chaos, intermittent and quasiperiodic routes to chaos as well as
period-adding sequences, Farey sequences, and so on. The chaotic dynamics is
verified by both experimental as well as computer simulation studies including
PSPICE.Comment: 4 pages, RevTeX 4, 5 EPS figure
Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit
We have identified the three prominent routes, namely Heagy-Hammel,
fractalization and intermittency routes, and their mechanisms for the birth of
strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic
system constructed using a negative conductance series LCR circuit with a diode
both numerically and experimentally. The birth of SNAs by these three routes is
verified from both experimental and their corresponding numerical data by
maximal Lyapunov exponents, and their variance, Poincar\'e maps, Fourier
amplitude spectrum, spectral distribution function and finite-time Lyapunov
exponents. Although these three routes have been identified numerically in
different dynamical systems, the experimental observation of all these
mechanisms is reported for the first time to our knowledge and that too in a
single second order electronic circuit.Comment: 21 figure
Observation of chaotic beats in a driven memristive Chua's circuit
In this paper, a time varying resistive circuit realising the action of an
active three segment piecewise linear flux controlled memristor is proposed.
Using this as the nonlinearity, a driven Chua's circuit is implemented. The
phenomenon of chaotic beats in this circuit is observed for a suitable choice
of parameters. The memristor acts as a chaotically time varying resistor
(CTVR), switching between a less conductive OFF state and a more conductive ON
state. This chaotic switching is governed by the dynamics of the driven Chua's
circuit of which the memristor is an integral part. The occurrence of beats is
essentially due to the interaction of the memristor aided self oscillations of
the circuit and the external driving sinusoidal forcing. Upon slight
tuning/detuning of the frequencies of the memristor switching and that of the
external force, constructive and destructive interferences occur leading to
revivals and collapses in amplitudes of the circuit variables, which we refer
as chaotic beats. Numerical simulations and Multisim modelling as well as
statistical analyses have been carried out to observe as well as to understand
and verify the mechanism leading to chaotic beats.Comment: 30 pages, 16 figures; Submitted to IJB
Unconventional Signals Oscillators
Dizertační práce se zabývá elektronicky nastavitelnými oscilátory, studiem nelineárních vlastností spojených s použitými aktivními prvky a posouzením možnosti vzniku chaotického signálu v harmonických oscilátorech. Jednotlivé příklady vzniku podivných atraktorů jsou detailně diskutovány. V doktorské práci je dále prezentováno modelování reálných fyzikálních a biologických systémů vykazujících chaotické chování pomocí analogových elektronických obvodů a moderních aktivních prvků (OTA, MO-OTA, CCII ±, DVCC ±, atd.), včetně experimentálního ověření navržených struktur. Další část práce se zabývá možnostmi v oblasti analogově – digitální syntézy nelineárních dynamických systémů, studiem změny matematických modelů a odpovídajícím řešením. Na závěr je uvedena analýza vlivu a dopadu parazitních vlastností aktivních prvků z hlediska kvalitativních změn v globálním dynamickém chování jednotlivých systémů s možností zániku chaosu v důsledku parazitních vlastností použitých aktivních prvků.The doctoral thesis deals with electronically adjustable oscillators suitable for signal generation, study of the nonlinear properties associated with the active elements used and, considering these, its capability to convert harmonic signal into chaotic waveform. Individual platforms for evolution of the strange attractors are discussed in detail. In the doctoral thesis, modeling of the real physical and biological systems exhibiting chaotic behavior by using analog electronic building blocks and modern functional devices (OTA, MO-OTA, CCII±, DVCC±, etc.) with experimental verification of proposed structures is presented. One part of theses deals with possibilities in the area of analog–digital synthesis of the nonlinear dynamical systems, the study of changes in the mathematical models and corresponding solutions. At the end is presented detailed analysis of the impact and influences of active elements parasitics in terms of qualitative changes in the global dynamic behavior of the individual systems and possibility of chaos destruction via parasitic properties of the used active devices.
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
In this set of lectures, we review briefly some of the recent developments in
the study of the chaotic dynamics of nonlinear oscillators, particularly of
damped and driven type. By taking a representative set of examples such as the
Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain
the various bifurcations and chaos phenomena associated with these systems. We
use numerical and analytical as well as analogue simulation methods to study
these systems. Then we point out how controlling of chaotic motions can be
effected by algorithmic procedures requiring minimal perturbations. Finally we
briefly discuss how synchronization of identically evolving chaotic systems can
be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in
Physics Please Lakshmanan for figures (e-mail: [email protected]
Autonomous Duffing-Holmes Type Chaotic Oscillator
A novel DuffingHolmes type autonomous chaotic oscillator is described. In comparison with the well-known nonautonomous DuffingHolmes circuit it lacks the external periodic drive, but includes two extra linear feedback subcircuits, namely a direct positive feedback loop, and an inertial negative feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations are presented. Fairly good agreement between numerical and experimental results is observed
Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force
We identify a novel route to the birth of a strange nonchaotic attractor
(SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal
(square wave) force as one of the quasiperiodic forces through numerical and
experimental studies. We find that bubbles appear in the strands of the
quasiperiodic attractor due to the instability induced by the additional square
wave type force. The bubbles then enlarge and get increasingly wrinkled as a
function of the control parameter. Finally, the bubbles get extremely wrinkled
(while the remaining parts of the strands of the torus remain largely
unaffected) resulting in the birth of the SNA which we term as the
\emph{bubbling route to SNA}. We characterize and confirm this birth from both
experimental and numerical data by maximal Lyapunov exponents and their
variance, Poincar\'e maps, Fourier amplitude spectra and spectral distribution
function. We also strongly confirm the birth of SNA via the bubbling route by
the distribution of the finite-time Lyapunov exponents.Comment: 11 pages. 11 figures, Accepted for publication in Phys. Rev.
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